Short answer
No, a single small bite of plain, cooked pasta is not an emergency and is generally safe for dogs. The real danger with pasta comes from common toppings like onion, garlic, or rich sauces, which are toxic. Since it was just a plain piece, the risk is very low. Simply monitor your dog for the next several hours. If they ate a large amount or you're unsure about the ingredients, watch for vomiting or lethargy and call your vet with any concerns.
Pasta — Food safety facts
Safe to share · Dogs · full breakdown on the linked food page
Plain cooked pasta is safe. Never with onion, garlic or pesto sauce.
The full verdict, portion guidance and serving notes are collected on the Pasta food facts page.